Thanks everybody, especially foxidrive
Following is the code which worked for me - perfectly so far
set backupcmd=xcopy /s /c /d /e /h /i /r /y
%backupcmd% "%AppData%\Thunderbird" "%CD%\Thunderbird"
It automatically copies Thunderbird folder from AppData and creates a folder named Thunderbird in the same directory where the batch file resides. The same code works on Win7, Win8, and WinXP. It does not matter which drive letter is assigned to my flash drive where the batch file resides.
Thanks to all of you